Gaussian random fields are completely characterized by their mean and
their covariance function. In applications suitable classes
of parametrized covariance functions are needed. Whilst in the
univariate case a large number of classes is available, not that many
classes exist in the multivariate case. In this talk we mainly focus
on bivariate covariance functios that are generalizations or
modifications of models that have been suggested by Tilmann Gneiting.
In particular, the univariate cutoff embedding technique is transferred
to the
bivariate case. On that way, the results for the univariate case had
to improved. As examples for the bivariate cutoff technique, we consider
Gneiting's bivariate Matern model and modifications thereof.
Finally, we show that Gneiting's generalized Cauchy model can be
combined with the fractional Browian motion to get a parametric model
that covers both the stationary and the intrinsically stationary case.